Adjacent Right Angles: Analyzing the Possibility of 90° Neighbors

Q: What does adjacent mean for angles?

Adjacent angles share a common vertex (corner point) and a common side (ray), but don't overlap. Think of them as neighbors that touch but don't cross over each other.

Q: Can two right angles really be next to each other?

Yes! When two $ 90° $ angles are adjacent on a straight line, they add up to $ 180° $, which is exactly what we expect for a straight line. This creates a perfectly straight line.

Q: How do I visualize two adjacent right angles?

Picture a straight horizontal line. Now draw a vertical line straight up from any point on it. You've created two $ 90° $ angles that are adjacent - one on the left and one on the right of the vertical line!

Q: Do adjacent angles always add up to 180°?

Only when they're on a straight line! Adjacent angles around a point add to $ 360° $, and adjacent angles in other shapes follow different rules depending on the shape.

Adjacent Angles with Straight Line Properties

It is possible for two adjacent angles to be right angles.

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Step-by-step video solution

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00:00 Can adjacent angles both be right angles?

00:03 Let's draw adjacent angles

00:07 Adjacent angles sum to 180° (straight angle)

00:11 Therefore, if one is right (90°), the other must also be right

00:15 To complete the straight angle (90°)

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

It is possible for two adjacent angles to be right angles.

Step-by-step solution

To determine if it is possible for two adjacent angles to be right angles, we start by considering the definition of adjacent angles. Adjacent angles share a common side and a common vertex. We must think about this scenario in terms of the angles lying on a straight line or a flat plane.

A right angle is exactly $90^\circ$ . Hence, if we have two right angles that are adjacent, their measures would be:

First angle: $90^\circ$
Second angle: $90^\circ$

When these two angles are adjacent, as defined in the problem, their sum is:

90^\circ + 90^\circ = 180^\circ

Angles that are adjacent along a straight line add up exactly to $180^\circ$ . Therefore, it is indeed possible for two adjacent angles to be both $90^\circ$ . This configuration simply means that these two angles lie along a straight line, dividing it into two right angles.

Hence, the statement is True.

Final Answer

True

Key Points to Remember

Essential concepts to master this topic

Definition: Adjacent angles share common vertex and side
Technique: Add measures: $90° + 90° = 180°$
Check: Sum equals straight line angle of exactly 180° ✓

Common Mistakes

Avoid these frequent errors

Assuming adjacent angles cannot both be 90°
Don't think that adjacent angles must be different sizes = wrong conclusion! This ignores that angles on a straight line sum to 180°. Always check if the sum equals 180° for adjacent angles on a line.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

What does adjacent mean for angles?

Adjacent angles share a common vertex (corner point) and a common side (ray), but don't overlap. Think of them as neighbors that touch but don't cross over each other.

Can two right angles really be next to each other?

Yes! When two $90°$ angles are adjacent on a straight line, they add up to $180°$ , which is exactly what we expect for a straight line. This creates a perfectly straight line.

What if the angles aren't on a straight line?

If adjacent angles aren't on a straight line, they can still both be $90°$ ! For example, in a rectangle, all four corner angles are $90°$ and adjacent angles share sides.

How do I visualize two adjacent right angles?

Picture a straight horizontal line. Now draw a vertical line straight up from any point on it. You've created two $90°$ angles that are adjacent - one on the left and one on the right of the vertical line!

Do adjacent angles always add up to 180°?

Only when they're on a straight line! Adjacent angles around a point add to $360°$ , and adjacent angles in other shapes follow different rules depending on the shape.

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